Wireless Power Transfer

John Ho
November 14, 2014

Submitted as coursework for PH240, Stanford University, Fall 2014


Fig. 1: Tesla's system of resonant coils for wireless power transfer. The coils are "tuned" to resonate using a capacitor, labeled "condenser". (Source: N. Tesla. [3,7])

The electronic devices and appliances that we use everyday are powered through conductive wires that guide electromagnetic energy from the point to point. Historical and modern interest in wireless power transfer stems from the possibility of eliminating such wires and yet still be able to harness electricity at any place and at any time. [1-6]


Wireless power transfer is mediated through a time-varying electromagnetic field. Its underlying mechanism been known since 1831 with the discovery of electromagnetic induction by Michael Faraday. In his original experiment, the motion of a magnet near a coil of wire induced a voltage across the two ends of a wire, which then drove a current through a galvanometer. Because no electrical contact exists between the magnet and the coil, energy in the motion of the magnet has been wirelessly transported into the circuit. The motion of the magnet relative to the circuit is essential for the transfer of power. According to Maxwell's equations, a changing magnetic field generates an electric field (and vice versa). This electric field is responsible for the voltage across the wire and ultimately power transferred to the circuit. Contrary to occasional misconception, power transfer cannot occur with a purely magnetic field. Indeed, the flow of power is given by a product of the electric and magnetic field (Poynting vector), so if the flow is to be continuous, no power can be transported by a purely electric or magnetic field.

There are two features in Faraday's original experiment that are important for understanding modern wireless power transfer systems. The first is that although the electric field is non-zero everywhere, the field is still predominantly magnetic in nature. Most everyday materials, including your body, do not interact with magnetic fields. As a result, this form of "magnetic" power transfer cannot be easily "blocked" by nearby objects. If a slab of wood is placed between the magnet and the coil, power is still transferred because biological tissue appears transparent to the magnetic field and, on the other side of the slab, the time-varying magnetic field still produces the electric field required to drive current in the circuit. Inevitably, however, some power is lost because an electric field is also generated inside slab, which interacts with wood by heating it. The second feature is that the amount of power extracted by the circuit depends on the electrical details of the galvanometer (or more generally, the "load" of the circuit). For example, if there is no load on the coil (i.e. leaving both ends of the wire in air) the electric field induces a voltage between the two ends, but is unable to drive any current through it. Power, given by the product between voltage and current, is not transferred to this circuit. In general, the choice of the load's impedance (ratio of voltage to current) plays an essential role in determining the efficiency of power transfer. [5,6] This problem is known among circuit engineers as impedance matching. [5]

Non-Radiative Transfer

Modern systems do not, of course, use a swinging magnet to transfer power. Power transfer using induction requires only a time-varying magnetic field. Such a field can be directly generated by taking another coil and driving it with a current that varies in time. Implemented this way, the magnetic field can be made to change much faster than a swinging magnet, easily a million times per second (megahertz frequencies). An important related length scale is λ, defined as the speed of light (3 x 108 meters/second) divided by the driving frequency (1/second). If the size of the coil is much less than λ, then the field around the coil remains magnetic in nature and qualitatively similar to the swinging magnet.

When current flows through the source coil, energy is stored in the magnetic field around it (as a circuit element, the coil is called an inductor). This field is confined closely to the source coil (sometimes called an evanescent field) and falls off rapidly with distance. A receive coil that intercepts some of the field is "coupled" to the source coil and can wirelessly extract power. Despite the rapid decrease in the field strength, power transfer can still be highly efficient because energy not transferred to the receive coil returns to the source coil. This energy is not lost. It can be stored in the electric field of the circuit, such as by using a capacitor. As energy is exchanged between the magnetic and electric fields, the stored energy can build up to large levels in a phenomenon known as resonance. [2,3,5] In the same manner, a resonance can be set up in the receive coil to enhance its interaction with the oscillating field. Such a system was developed and popularized by Nikola Tesla in the early 1900s. [3] The efficiency in such a system is ultimately limited by the intrinsic losses in the coils and the environment (both in material and radiation). In this mode, the maximum range for high efficiency power transfer is typically less than 3 to 4 times the diameters of the coils. An efficiency of 40% was reported by Brown when transferring 60 W over 2 m. [4] About 5 W was radiated (see next section), while the remaining power is dissipated in the coils and in the surrounding environment.

Radiative Transfer

If the driving frequency increases to the point where the coil size is comparable to the number λ (near the gigahertz range for a coil several centimeters in diameter), the characteristics of power transfer substantially change. As the current through the coil oscillates faster, the magnetic field changes more rapidly and generates a larger electric field. The electric field itself also changes in time and, following Maxwell's equations, in turn also generates time-varying magnetic field. This interplay between the magnetic and electric fields can result in self-sustaining patterns of oscillations that move away from the source at the speed of light. The source is said to "radiate" while the fields "propagate" and continuously transport energy away.

Sources designed to generate propagating fields are known as antennas and are used everyday to transfer information in cell phones and radio. Using such radiative structures, the range of power transfer can in principle be much greater because the fields are not held near the source. [4] There are, however, important technical disadvantages for radiative power transfer compared to the non-radiative mode. For radiative sources, the direction of radiation is important because energy is transported away whether or not there are interacting objects in that direction. To prevent power from being radiated in all directions, strategies for narrowing a beam of radiation and tracking the target point are needed. Because of the intertwined nature of the electric and magnetic field, energy transport can also be easily "blocked" by objects, even if they only interact with the electric field. One demonstration showed that 30 kW could be transmitted across 1 mi using large (288 ft2) antennae with laboratory-measured efficiency of 54%. [4]

As historical note, Tesla built and demonstrated systems for non-radiative power transfer, but was opposed to the idea that propagating fields could be useful for power transfer. [3] His most well-known work on power transfer was instead based on the flawed idea that the earth and the atmosphere could be used as a conductive path for effectively transferring power. His set of experiments involved spectacular "Tesla coils" intended to generate sufficiently high voltages to establish such a path. [2,4]

© John Ho. The author grants permission to copy, distribute and display this work in unaltered form, with attribution to the author, for noncommercial purposes only. All other rights, including commercial rights, are reserved to the author.


[1] N. Tesla, "Method of Regulating Apparatus For Producing Currents of High Frequency," U.S. Patent 568,178, September 1896.

[2] N. Tesla, "Apparatus for Transmitting Electrical Energy," U.S. Patent 1,119,732, December 1914.

[3] N. Tesla, "The True Wireless," Electrical Experimenter 7, No. 1, 23 (May 1919).

[4] W. C. Brown, "The History of Power Transmission by Radio Waves," IEEE Trans. Microw. Theory Techn., 32, 1230, (1984).

[5] A. Kurs et al., "Wireless Power Transfer via Strongly Coupled Magnetic Resonances," Science, 317, 83 (2007).

[6] S. Y. R. Hui, et al., "A Critical Review of Recent Progress in Mid-Range Wireless Power Transfer," IEEE Trans. Power Electronics 29, 4500 (2014).

[7] "Duration of Copyright," U.S. Copyright Office, Circular 15a, August 2011.